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Distribution of functionals of bridges for diffusions with jumps

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Abstract

The paper deals with a method of calculation of distributions for functionals of bridges of a process which is a generalization of a diffusion with jumps. The approach to calculation of distributions for integral functionals of bridges is the same as for the diffusion itself. This approach is based on calculation of the Laplace transform of distributions of the integral functionals. Bibliography: 4 titles.

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References

  1. A. N. Borodin, “Distribution of functionals of distributions with jumps,” Zap. Nauchn. Semin. POMI, 339, 15–36 (2006).

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  2. M. Kac, “On some connections between probability theory and differential and integral equations,” in: Proc. Second Berkeley Symp. Math. Stat. Probab. (1951), pp. 189–215.

  3. E. Mordecki, “Ruin probabilities for Lévy processes with mixed exponential negative jumps, ” Teor. Veroyatn. Primen., 48, 188–194 (2003).

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  4. A. V. Skorokhod, Random Processes with Independent Increments [in Russian], Moscow (1964).

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Correspondence to A. N. Borodin.

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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 341, 2007, pp. 34–47.

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Borodin, A.N. Distribution of functionals of bridges for diffusions with jumps. J Math Sci 147, 6864–6872 (2007). https://doi.org/10.1007/s10958-007-0509-3

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  • DOI: https://doi.org/10.1007/s10958-007-0509-3

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